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Q: Which describes the average velocity of a bicycle going at a constant speed in a constant direction?

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If, as you say, its acceleration is "constant", then the average is exactly equal to that constant.

The total displacement divided by the time. The slope of the displacement vs. time graph.

Velocity is speed and its direction. Average velocity is average speed and its direction.

The term "velocity", as used in physics, DOES have an associated direction. Most derived terms, such as "average velocity", also do.

Direction. Velocity has speed and direction

In that case, the average speed is the same as the instantaneous speed.

There are several definitions. not just one. Average velocity in a direction = Average displacement (distance) in that direction/time Instantaneous velocity in a direction = derivative of displacement in that direction with respect to time Average velocity in a direction = Initial velocity in that direction + Average acceleration in that direction * time Instantaneous velocity in a direction = Definite integral of acceleration in that direction with respect to time, with initial velocity at t = 0 Then there are others in which time is eliminated.

Yes, if the instantanious velocity is constant.

No. If it its moving at constant velocity, its instantaneous velocity would be the same as its constant velocity.

If the velocity is constant (i.e., there is no acceleration). Terminal velocity is an example, although any constant velocity would fit this description.

Only if the velocity is constant.

average speed.

The accleration must be constant.

The magnitude of average velocity of an object equal to its average speed if that object is moving with CONSTANT velocity.

Avg velocity is the speed you are going. Constant acceleration is the rate you increase your speed. = =

The question is inherantly flawed. A car traveling at a constant speed cannot accelerate, if it could it's speed would not be constant. "Constant speed" means that speed is not increasing or decreasing but remain consistent over time. For example, if you cover 10 feet during each second, your speed is constant. "Constant velocity" implies constant speed, but it has an additional constraint: you can't change your direction. If you travel constantly at 10 feet per second in a straight line, then your speed is constant and your velocity is constant. But if you travel constantly at 10 feet per second in a wiggly line (or a circle, or anything not straight), then your speed is constant but your velocity is NOT constant. If you travel at a constant speed but change direction, velocity is changed. Or if you travel in the same direction but change the speed, velocity is changed. Average speed is is easier: distance/time So, your question should read: Why can a car traveling at an average speed accelerate, but a car traveling at constant speed cannot? Or Why am I asking the wrong questions?

The average velocity in a particular direction = distance travelled in that direction / time taken. Velocity is a vector so the direction is important. If I go from A to B and then return to A my average velocity will be zero. My speed, on the other hand, will not be zero.

Yes - just like any velocity, average velocity is a vector and has a direction associated with it. Speed, on the other hand is only an intensive property which has no specific direction associated with it. You could consider speed to be the magnitude of the velocity vector.

This describes the average speed. If there is a direction specified that the distance has moved, then it will be a vector, and called average velocity.

In order to find an average velocity, you need an average speed and an average direction. Average speed = (distance traveled) divided by (time to travel that distance) Average direction could be defined as the direction from the starting point to the end point.

Average velocity equals the average speed if (and only if) the motion is in the same direction. If not, the average speed, being the average of the absolute value of the velocity, will be larger.

Mainly when the velocity is constant.

It means that an object with a negative average velocity is moving in the opposite direction (of course according to the chosen positive direction of the predefined frame).

That is the case when you are talking about instantaneous speed and velocity - or when the velocity is constant. In the case of an average speed and velocity, this relation does not hold.

Average velocity in a direction is calculated as the displacement in that direction divided by the total time taken. As the time interval is reduced, the displacement over that period also reduces and the limiting value of that ratio is the instantaneous velocity.

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